TY - JOUR
T1 - Optimal Error Estimate of Fourier Spectral Method for the Kawahara Equation
AU - Deng , Zhenguo
JO - Journal of Mathematical Study
VL - 3
SP - 291
EP - 306
PY - 2017
DA - 2017/09
SN - 50
DO - http://doi.org/10.4208/jms.v50n3.17.06
UR - https://global-sci.org/intro/article_detail/jms/10622.html
KW - Fourier spectral method, Kawahara equation, error estimate.
AB - <p style="text-align: justify;">An optimal error estimate in $L^2$-norm for Fourier spectral method is presented
for the Kawahara equation with periodic boundary conditions. A numerical
example is provided to confirm the theoretical analysis. The method and proving skills
are also applicable to the periodic boundary problems for some nonlinear dispersive
wave equations provided that the dispersive operator is bounded and antisymmetric
and commutes with differentiation.</p>